Parametric critical path analysis for event networks with minimal and maximal timelags

High-end manufacturing systems are cyber-physical systems where productivity depends on the close cooperation of mechanical (physical) and scheduling (cyber) aspects. Mechanical and control constraints impose minimal and maximal time differences between events in the product flow. Sequence-dependent constraints are used by a scheduler to optimize system productivity while satisfying operational requirements. The numerous constraints in a schedule are typically related to a relatively small set of parameters, such as speeds, lengths, or settling times. We contribute a parametric critical path algorithm that identifies bottlenecks in terms of the feasible parameter combinations. This algorithm allows analysis of schedules to identify bottlenecks in terms of the underlying cause of constraints. We also contribute a way to find Pareto-optimal cost-performance trade-offs and their associated parameter combinations. These results are used to quantify the impact of relaxing constraints that hinder system productivity.